Magnetic resonance is a known technique by which images of the interior of an examination object can be produced. In this case, the relationship between the precession frequencies (Larmor frequencies) of excited spins and the magnetic field strength of the magnetic field in the magnetic resonance scanner is used for position resolution. The magnetic field that is used is in this case composed of the basic magnetic field of the magnetic resonance scanner and applied gradient magnetic fields. Normal methods for reconstruction of image data records from magnetic resonance signals are predicated on a homogeneous basic magnetic field and strictly linear gradient magnetic fields.
The relationship between the Larmor frequencies and the magnetic field that is used results in geometric distortion along the frequency coding direction (read direction) in the image data records obtained from the magnetic resonance signals, if there are any inhomogeneities in the basic magnetic field. If there are non-linearities in the gradient fields, the distortion occurs not only on the tomographic image plane but also at right angles to this in the case of slice stimuli with a selection gradient. In practice, such inhomogeneities in the basic magnetic field and non-linearities in the gradient fields cannot be avoided completely. Nevertheless, the discrepancies in the basic magnetic field, that is to say the inhomogeneity, within a measurement volume of a magnetic resonance scanner should be less than three parts per million (ppm).
The resultant distortion in this case relates not only to the geometric position of the image data reconstructed from the magnetic resonance signals, but also to the reconstructed image signal strength. Attenuation of the image signal strength can occur in this case, for example, by dephasing of the spins in the presence of strong local basic field inhomogeneities. Further corrupting changes in the image signal strength are possible as a result of the spatial distribution of the intensity values, determined from the magnetic resonance signals, on an area whose size differs from the actual area.
The reasons why inhomogeneities occur in basic magnetic fields in magnetic resonance scanners are, for example, linked to the design, that is to say they are dependent, for example, on the design and winding geometry of the basic field magnet, the shielding and any shim apparatuses that are present. Inhomogeneities in the basic magnetic field caused in this way are static, that is to say they remain essentially constant over time.
In order to determine the inhomogeneity of the basic magnetic field, the magnetic field which actually occurs, for example, is measured at a plurality of measurement points on the surface of the measurement volume with the aid of magnetic field sensors, for example Hall sensors, of the measurement phantom.
If the measurement points lie on a spherical surface with a radius r0, the coefficients Al,m and Bl,m, which are also referred to as a “spectrum” of the following development function can be calculated using spherical functions of magnetic fields. Using said development function:
      B    ⁢                  ⁢    0    ⁢          (              r        ,        ϑ        ,        φ            )        =            ∑              l        =        0            ∞        ⁢                            (                      r                          r              0                                )                l            ⁢                        ∑                      m            =            0                    l                ⁢                                            P                              l                ,                m                                      ⁡                          (                              cos                ⁢                                                                  ⁢                ϑ                            )                                ⁢                      (                                                            A                                      l                    ,                    m                                                  ⁢                                  cos                  ⁡                                      (                                          m                      ⁢                                                                                          ⁢                      φ                                        )                                                              +                                                B                                      l                    ,                    m                                                  ⁢                                  sin                  ⁡                                      (                                          m                      ⁢                                                                                          ⁢                      φ                                        )                                                                        )                              the total basic magnetic field B0 can then be calculated from this at any point (r,υ,φ) (spherical coordinates) within the measurement volume. Pl,m in this case denotes the normalized Legendré functions associated with the Legendré polynomials P1.
Any local discrepancy of the basic magnetic field ΔB0(r,υ,φ)=B0(r,υ,φ)−B0nom can be calculated from the calculated values B0(r,υ,φ) and the nominal value for the basic magnetic field B0nom.
The basic field inhomogeneity can also be calculated as the relative basic field inhomogeneity δB0 at any point (r,υ,φ):
            δ              B        ⁢                                  ⁢        0              ⁡          (              r        ,        ϑ        ,        φ            )        =                              B          ⁢                                          ⁢          0          ⁢                      (                          r              ,              ϑ              ,              φ                        )                          -                  B          ⁢                                          ⁢                      0            nom                                      B        ⁢                                  ⁢                  0          nom                      =                            Δ                      B            ⁢                                                  ⁢            0                          ⁡                  (                      r            ,            ϑ            ,            φ                    )                            B        ⁢                                  ⁢                  0          nom                    
The distribution of the relative basic field inhomogeneity can be stored on a position-resolved basis in a so-called B0 map. A B0 map such as this may, for example, be represented as a height profile on a slice plane through the measurement volume. In this case, the height profile indicates the relative basic field inhomogeneity at the respective location in the measurement volume.
Further reasons for inhomogeneities of a magnetic field in a magnetic resonance scanner are, for example, susceptibility changes caused by an examination object being introduced into the magnetic resonance scanner, dynamic disturbances caused by eddy currents or artefacts such as “chemical shift”, liquid artefacts or movements of the examination object. Inhomogeneities caused in this way depend on the respective situation, for example the nature of the examination and of the examination object.
All types of distortion in image data records are undesirable, in particular in medical image data records, since they corrupt a diagnosis, or at least make it harder and, for example, make it harder to determine the absolute position of a lesion. Because of the various possible causes and types of distortion, various methods already exist to correct for the various types of distortion in image data records.
One method for distortion correction for gradient non-linearities in magnetic resonance scanners is known from DE 195 40 837 B4. In this case, two auxiliary data records which describe a shift of a measured point with respect to an actual point of a signal origin are used to carry out position corrections in the x and y directions. Intensity corrections are also used, in addition to the position corrections.
DE 198 29 850 C2 describes a method for reconstruction of a planar slice image from magnetic resonance signals in inhomogeneous magnetic fields. In this case, image elements of a planar slice image are produced from a plurality of original image elements on curved slices in the examination object.
WO 95/30908 A1 describes a method in which a generalized Fresnel transformation (GFT reconstruction) is carried out in the read direction. The GFT reconstruction takes account of any known position dependency of the main magnetic field in the read direction in order to allow distortion and intensity errors to be corrected for during the transformation from the measurement data space (k space) to the position space.
There is also a requirement for powerful methods for correction for distortion in image data records recorded by means of magnetic resonancing.